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# $S$ and $T$ are points on sides $PR$ and $QR$ of $âˆ†PQR$ such that $\angle P = \angle RTS$. Show that $âˆ†RPQ \sim âˆ†RTS$.

Given:

$S$ and $T$ are points on sides $PR$ and $QR$ of $∆PQR$ such that $\angle P = \angle RTS$.

To do:

We have to show that $∆RPQ \sim ∆RTS$.

Solution:

In $\triangle RPQ$ and $\triangle RTS$,

$\angle P=\angle RTS$

$\angle P=\angle R$

Therefore, by AA criterion,

$\Delta RPQ \sim \Delta RTS$

Hence proved.

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